Time series motif discovery has emerged as perhaps the most used primitive for time series data mining, and has seen applications to domains as diverse as robotics, medicine and climatology. There has been recent significant progress on the scalability of motif discovery. However, we believe that the current definitions of motif discovery are limited, and can create a mismatch between the user's intent/expectations, and the motif discovery search outcomes. In this work, we explain the reasons behind these issues, and introduce a novel and general framework to address them. Our ideas can be used with current state-of-the-art algorithms with virtually no time or space overhead, and are fast enough to allow real-time interaction and hypotheses testing on massive datasets. We demonstrate the utility of our ideas on domains as diverse as seismology and epileptic seizure monitoring.